[seqfan] Re: symmetric 0-1 matrices
Paul D Hanna
pauldhanna at juno.com
Thu Feb 3 08:31:49 CET 2011
Another formula:
Sum_{k>=0..n^2} k*SM(n,k) = n^2/2 * 2^(n(n+1)/2).
and there are probably many more! So I'll stop here.
---------- Original Message ----------
From: "Paul D Hanna" <pauldhanna at juno.com>
To: seqfan at list.seqfan.eu
Subject: [seqfan] Re: symmetric 0-1 matrices
Date: Thu, 3 Feb 2011 07:06:16 GMT
And I added the following formulae along with PARI code (not yet published):
G.f. of row n: (1+x^2)^(n(n-1)/2)*(1+x)^n for n>=1.
G.f.: A(x,y) = Sum_{n>=1} x^n*(1+y)^n*Product_{k=1..n} (1-x(1+y)(1+y^2)^(2k-2))/(1-x(1+y)(1+y^2)^(2k-1)) due to a q-series identity.
The g.f. of row n may be obvious from Brendan's formula, but the g.f. A(x,y) is a nice series representation that follows directly from it.
Paul
---------- Original Message ----------
From: "N. J. A. Sloane" <njas at research.att.com>
To: seqfan at list.seqfan.eu
Subject: [seqfan] Re: symmetric 0-1 matrices
Date: Thu, 3 Feb 2011 01:14:28 -0500
I added that triangle to the OEIS - see A184948.
Neil
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